Free vibration of functionally graded sandwich plates using four-variable refined plate theory

Abstract

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.

Thermoelastic Deflection Responses of CNT Reinforced Sandwich Shell Structure using Finite Element Method

“…As discussed earlier, the HSDT kinematics is further utilised to model the and sandwich and laminated composite panel to compute the static and the dynamic behaviour by Mantari et al [34]. Further, the free vibration frequencies of the FG sandwich structure evaluated computationally by Hadji et al [35] using a refined classical laminated plate theory including four-variables. Khalili and Mohammadi [36] reported thermal free vibration frequency responses of the FG sandwich plate structure.…”

Analysis of functionally graded sandwich plates using a new first-order shear deformation theory

“…To reduce computational cost, HSDTs with four unknowns were recently developed for FG sandwich plates (see Refs. [14][15][16][17][18][19][20][21]). …”

Free vibration of functionally graded sandwich plates with stiffeners based on the third-order shear deformation theory

“…Integrals in Eqs. (46)- (47) and (55) will be computed by Gauss quadrature [11]. The program for solving Eq.…”

“…The material properties, as given in L. Hadji [11] are E m = 70 GPa, ν m = 0.3, ρ m = 2707 kg/m 3 for Al; E c = 380 GPa, ν c = 0.3, ρ c = 3800 kg/m 3 for Al 2 O 3 ; Thickness relation is denoted as the top layer thickness -the core thickness -the bottom thickness = 1-1-1. The dimensionless frequencies = ωa 2 /(2h) ρ 0 /E 0 (where ρ 0 = 1 kg/m 3 , E 0 = 1 GPa) obtained by the present paper are compared with the first-order shear deformation plate theory (FSDT) (analytical method), the third-order shear deformation plate theory (TSDT) (analytical method), and the four-variable refined plate theory [11] (analytical method) in Tab. 2.…”